The Hitchin fibration has already found many beautiful applications to representation theory, such as Cherednik algebras and automorphic representations. Using the recent work of Bezrukavnikov-Boixeda Alvarez-Shan-Vasserot relating the invariant part of the center of the small quantum group to the geometry of a specific singular Hitchin fiber, we prove a conjecture of Igor Frenkel describing the dimension of the center. Furthermore, when G is of type A, we prove (conditionally on a conjecture of Carlsson-Mellit) that there is a bigraded structure on the center, coinciding with Haiman’s diagonal coinvariant ring. This is joint work with Anna Lachowska and Nicolas Hemelsoet.
By Alexander Soibelman
By Mingkun Liu
By Pierrick Bousseau
By Anna Barbieri
By Gabriele Rembado
By Pierrick Bousseau
By Joshua Lam
By Oscar Kivinen
By Elba Garcia-Failde
By Nezhla Aghaei
By Carlos Simpson
By Claudio Dappiaggi
